OPTIMIZED CALCULATION OF A QUADRATIC MODEL FOR SPEED DEPENDENT LINESHAPES

\underline{KENDRA L. LETCHWORTH}, D. CHRIS BENNER, Department of Physics, The College of William and Mary, Williamsburg, VA, 23187-8795.

A new algorithm for computation of a speed dependent lineshape function is presented. The lineshape that is calculated is based upon a quadratic model for the Lorentz width as a function of velocity. The calculation includes both real and imaginary parts of the lineshape for applications to line mixing and Dicke narrowing. This algorithm sacrifices a small amount of memory space for a considerable gain in speed and accuracy and employs methods similar to the techniques used to calculate the Voigt Profile as described by Letchworth and Benner^{a}. For Lorentz widths greater than about five times the Doppler width and for points more than about five Doppler widths from the center of the spectral line, Gauss-Hermite quadrature is employed. For most other cases, a Taylor series expansion about the nearest point in a precomputed table is used. In some cases where the Doppler width is more than an order of magnitude larger than the Lorentz width, Lagrange interpolating polynomials are used with a table of precomputed points. The accuracy is one part in 10^{5} of the value of the function itself. Optionally, derivatives with respect to certain lineshape parameters are also returned. The algorithm provides a good approximation for speed dependent lineshapes with a calculation time which is not significantly larger than the time required to calculate the Voigt Profile using the Drayson^{b}, Humlicek^{c}, and Letchworth and Benner routines. This material is based upon work supported by the National Science Foundation under Grant No. ATM-0338475.

aK. L. Letchworth, D. C. Benner J. Quant. Spectrosc. Radiat. Trans. In Press.

bS. R. Drayson J. Quant. Spectrosc. Radiat. Trans. \underline{16}, 611-614, 1976.

cJ. Humlicek J. Quant. Spectrosc. Radiat. Trans. \underline{27}, 437-444, 1982.